The discrete nonlinear Schrödinger equation (REF ) is defined on
the one-dimensional lattice. It is generalized to a nonlinear equation on an
arbitrary lattice[1]}, [2]}, [3]},
\(i\frac{d\psi _{n}}{dt}+\sum _{m=1}^{N}M_{nm}\psi _{m}+\xi \left|\psi _{n}\right|^{2}\psi _{n}=0, \) 
